A Constrained Top-Down Argument for R-Parity Conservation

We argue that R-parity violation (RPV) is excluded in a large class of realistic four dimensional models with an SU(5) GUT that could be obtained from string/M theory, including phenomenologically viable M-theory compactifications with an SU(5) GUT. We reach this conclusion by studying supersymmetric SU(5) GUTs in a general context. We prove that any SU(5) GUT theory with an abelian flavor symmetry commuting with SU(5) that gives rise to consistent fermion masses and mixings and which allows for any trilinear RPV, must also allow for bilinear RPV. Furthermore, in models where the mechanisms of supersymmetry breaking and mediation are known to generate a viable mu term, i.e. solving the doublet-triplet splitting and mu-Bmu problems, it can be shown that bilinear RPV terms, if allowed, are generically generated at the same order as that of the mu term. Then the stringent constraints on bilinear RPV from neutrino masses implies that R-parity violation is strongly disfavored in such models. M-theory compactifications with an SU(5) GUT provide a well-motivated class of models with the above features. These conclusions may be avoided in GUTs based on SO(10) or E_6, but it seems to be particularly challenging to do so with reasonable dynamical assumptions. The conclusion is that any observation of R-parity violation at the LHC should strongly disfavor such classes of models.